The post specifically explained why your properties cannot be used for predictions in the context of doomsday argument and sleeping beauty problem. I would like to know your thoughts on that.
I will just post the relationship between perspective reasoning and simulation argument here.
In 2003 Nick Bostrom published his paper “Are you living in a computer simulation?”. In that paper he suggested once a civilization reaches a highly developed state it would have enough computing power to run “ancestral simulations”. Such simulations would be indistinguishable from actual reality for its occupants. Furthermore, because the potential number and levels of such simulated realities is huge, almost all observers with experiences similar to ours would b...
Yes, that's why I think to this day Elga's counter argument is still the best.
No problem, always good to have a discussion with someone serious about the subject matter.
First of all, you are right: statistic estimation and expected value in bayesian analysis are different. But that is not what I'm saying. What I'm saying is in a bayesian analysis with an uninformed prior (uniform) the case with highest probability should be the unbiased statistic estimation (it is not always so because round offs etc).
In the two urns example, I think what you meant is that using the sample of 4 balls a fair estimation would be 5 reds and 15 blues a...
Thank you for the reply. I really appreciate it since it reminds me that I have made a mistake in my argument. I didn't say SSA means reasoning as if an observer is randomly selected from all actually existent observers ( past, present and /b/future/b/).
...So how do you get Beauty's prediction? If at the end of the first day you ask for a prediction on the coin, but you don't ask on the second day, then now Beauty knows that the coin flip is, as you say, yet to happen, and so she goes back to predicting 50/50. She only deviates from 50/50 when she thinks t
Ok, I should have use my words more carefully. We meant the same thing. When I say beauty think the 8 rooms are unbiased sample I meant what I listed as C: It is an unbiased for the other 80 rooms. So yes to what you said, sorry for the confusion. it is obvious because it is a simple random sample chosen from the 80 rooms. So that part there is no disagreement. The disagreement between the two is about whether or not the 9 rooms are an unbiased sample. Beauty as a thirder should not think it is unbiased but bases her estimation on it anyway to answer the q...
Very clear argument and many good points. Appreciate the effort.
Regarding your position on thirders vs halfers, I think it is a completely reasonable position and I agree with the analysis about when halfers are correct and when thirders are correct. However to me it seems to treat Sleeping Beauty more as a decision making problem rather than a probability problem. Maybe one's credence without relating consequences is not defined. However that seems counter intuitive to me. Naturally one should have a belief about the situation and her decisions should dep...
Yes, I have given a long run frequency argument for halving in part I. Sadly that part have not gotten any attention. My entire argument is about the importance of perspective disagreement in SBP. This counter argument is actually the less important part.
OK, I misunderstood. I interpreted the coin is biased 1/3 to 2/3 but we don't know which side it favours. If we start from uniform (1/2 to H and 1/2 to T), then the maximum likelihood is Tails.
Unless I misunderstood again, you mean there is a coin we want to guess its natural chance (forgive me if I'm misusing terms here). We do know its chance is bounded between 1/3 and 2/3. In this case yes, the statistical estimate is 0 while the maximum likelihood is 1/3. However it is obviously due to the use of a informed prior (that we know it is between 1/3 and 2...
Maximum likelihood is indeed 0 or Tails, assuming we start from a uniform prior. 1/3 is the expected value. Ask yourself this, after seeing a tail what should you guess for the next toss result to have maximum likelihood of being correct?
If halfers reasoning applies to both Bayesian and Frequentist while SIA is only good in Bayesian isn't it quite alarming to say the least?
Nothing shameful on that. Similar arguments, which Jacob Ross categorized as "hypothetical priors" by adding another waking in case of H, have not been a main focus of discussion in literatures for the recent years. I would imagine most people haven't read that.
In fact you should take it as a compliment. Some academic who probably spent a lot of time on it came up the same argument as you did.
Appreciate the effort. Especially about the calculation part. I am no expert on coding. But from my limited knowledge on python the calculation looks correct to me. I want to point out for the direct calculation formulation like this+choose+3)++((81-r)+choose+6)),+r%3D3+to+75)+%2F+(sum+(+((r)+choose+3)++((81-r)+choose+6)),+r%3D3+to+75)) gives the same answer. I would say it reflect SIA reasoning more and resemble your code better as well. Basically it shows under SIA beauty should treat her own room the same way as the other 8 rooms.
The part explaining th...
For the priors,. I would consider Beauty's expectations from the problem definition before she takes a look at anything to be a prior, i.e. she expects 81 times higher probability of R=81 than R=1 right from the start.
In the original sleeping beauty problem, what is the prior for H according to a thirder? It must be 1/2. In fact saying she expects 2 times higher probability of T than H right from the start means she should conclude P(H)=1/3 before going to sleep on Sunday. That is used as a counter argument by halfers. Thirders are arguing after waking ...
This argument is the same as Cian Dorr's version with a weaker amnesia drug. In that experiment a weaker amnesia drug is used on beauty if Heads which only delays the recollection of memory for a few minutes, just like in your case the memory is delayed until the message is checked.
This argument was published in 2002. It is available before majority of the literature on the topic is published. Suffice to say it is not convincing to halfers. Even supporter like Terry Horgan admit the argument is suggestive and could run a serious risk of slippery slope.
In both boy or girl puzzle and Monty hall problem the main point is "how" the new information is obtained. Is the mathematician randomly picking a child and mentioning its gender, or is he purposely checking for a boy among his children. Does the host know what's behind the door and always reveal a goat, or does he simple randomly opens a door and it turns out to be a goat. Or in statistic terms: how is the sample drawn. Once that is clear bayesian and statistics gives the same result. Of course if one start from a wrong assumption about the samp...
Both claims are very bold, both unsubstantiated.
First of all, SIA in bayesian is up to debate. That's the whole point of halfer/thirder disagreement. A "consistent" reasoning is not necessarily correct. Halfers are also consistent.
Second of all, the statistics involved is as basic as it gets. You are saying with a simple random sample of 9 rooms with 3 reds, it is wrong to estimate the population have 30% reds. Yet no argument is given.
Also please take no offence, but I am not going to continue this discussion we are having. All I have been doing is explaining the same points again and again. While the replies I got are short and effortless. I feel this is no longer productive.
Ok, let's slow down. First of all there are two type of analysis going on. One is bayesian analysis which you are focusing on. The other is simple statistics, which I am saying thirders and SIA are having troubles with.
If there are 100 rooms either red or blue. You randomly open 10 of them and saw 8 red and 2 blue. Here you can start a bayesian analysis (with an uniform prior obviously) and construct the pdf. I'm going to skip the calculation and just want to point out R=80 would have the highest probability. Now instead of going the bayesian way you can a...
Thirder and the selector have the exact same prior and posteriors. Their bayesian analysis are exactly the same.
Think from the selector's perspective. He randomly opens 9 out of the 81 rooms and found 3 red. Say he decided to perform a bayesian analysis. As stated in the question he starts from an uniform prior and updates it with the 9 rooms as new information. I will skip the calculation but in the end he concluded R=27 has the highest probability. Now think from the thirder's perspective. As SIA states she is treating her own room as randomly selected ...
Maybe it is my English. In this case, you wake up in a red room, and open another room and found it to be blue. As SIA states, you should treat both rooms as they are randomly selected from all rooms. So in the 2 randomly selected rooms 1 is red and 1 is blue. Hence 50%.
Sure. Although I want to point out the estimation would be very rough. That is just the nature of statistics with very small sample size.
The "beans in the hand" would be the random other room you open. The "beans in the bag" would be the two other rooms.
Let's say you open another room and found it red. If I'm correct as a thirder you would give R=3 a probability of 3/4, R=2 a probability of 1/4. This can be explained by SIA: this is randomly selecting 2 rooms out of the 3 and they are both red. 3 ways for it to happen if R=3 and 1 way...
Very clear argument, thank you for the reply.
The question is if we do not use bayesian reasoning, just use statistics analysis can we still get an unbiased estimation? The answer is of course yes. Using fair sample to estimate population is as standard as it gets. The main argument is of course what is the fair sample. Depending on the answer we get estimation of r=21 or 27 respectively.
SIA states we should treat beauty's own room as a randomly selected from all rooms. By applying this idea in bayesian analysis is how we get thirdism. To oversimplify it:...
Imagine a bag of red and blue beans. You are about to take a random sample by blindly take a handful out of the bag. All else equal, one should expect the fraction of red beans in your hand is going to be the same as its fraction in the bag. Now someone comes along and says based on his calculation you are most likely to have a lower faction of red beans in your hand than in the bag. He is telling you this even before you deciding where in the bag you are going to grab. He is either (a) having supernatural predicting power or (b) wrong in his reasoning.
I think it is safe to say he is wrong in his reasoning.
What you said is correct. I'm arguing because the 8 rooms is obviously an unbiased sample, the 9 rooms cannot be. Which means beauty cannot treat her own room as a randomly selected room from all rooms as SIA suggests. The entire thought experiment is a reductio against thirders in the sleeping beauty problem. It also argues that beauty and the selector, even free to communicate and having identical information, would still disagree on the estimation of R.
First thing I want to say is that I do not have a mathematics or philosophy degree. I come from an engineering background. I consider myself as a hobbyist rationalist. English is not my first language, so pease forgive me when I make grammar mistakes.
The reason I've come to LW is because I believe I have something of value to contribute to the discussion of the Sleeping Beauty Problem. I tried to get some feedback by posting on reddit, however maybe due to the length of it I get few responses. I find LW through google and the discussion here is much more ...
The doomsday argument is controversial not because its conclusion is bleak but because it has some pretty hard to explain implications. Like the choice of reference class is arbitrary but affects the conclusion, it also gives some unreasonable predicting power and backward causations. Anyone trying to understand it would eventually have to reject the argument or find some way to reconcile with these implications. To me neither position are biased as long as it is sufficiently argued.